Proceedings 38th Annual Symposium on Foundations of Computer Science

20-22 Oct. 1997

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  • Proceedings 38th Annual Symposium on Foundations of Computer Science

    Publication Year: 1997
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    Freely Available from IEEE
  • Author index

    Publication Year: 1997, Page(s):605 - 606
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    Freely Available from IEEE
  • On the power of quantum finite state automata

    Publication Year: 1997, Page(s):66 - 75
    Cited by:  Papers (64)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (816 KB)

    In this paper, we introduce 1-way and 2-way quantum finite state automata (1qfa's and 2qfa's), which are the quantum analogues of deterministic, nondeterministic and probabilistic 1-way and 2-way finite state automata. We prove the following facts regarding 2qfa's. 1. For any ε>0, there is a 2qfa M which recognizes the non-regular language L={ambm|m⩾1} with (one-s... View full abstract»

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  • An improved algorithm for quantifier elimination over real closed fields

    Publication Year: 1997, Page(s):56 - 65
    Cited by:  Papers (7)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (864 KB)

    We give a new algorithm for quantifier elimination in the first order theory of real closed fields that improves the complexity of the best known algorithm for this problem till now. Unlike previously known algorithms the combinatorial part of the complexity of this new algorithm is independent of the number of free variables. Moreover, under the assumption that each polynomial in the input depend... View full abstract»

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  • The computational complexity of knot and link problems

    Publication Year: 1997, Page(s):172 - 181
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (912 KB)

    We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted (that is, whether it is capable of being continuously deformed without self-intersection so that it lies in a plane). We show that this problem, UNKNOTTING PROBLEM, is in NP. We also consider the problem, SPLITTING PROBLEM, of determining whether two or more such polygons can be split (that i... View full abstract»

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  • Deciding properties of polynomials without factoring

    Publication Year: 1997, Page(s):46 - 55
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (888 KB)

    The polynomial time algorithm of Lenstra, Lenstra, and Lovasz (1982) for factoring integer polynomials and variants thereof have been widely used to show that various computational problems in number theory have polynomial time solutions. Among them is the problem of factoring polynomials over algebraic number fields, which is used itself as a major subroutine for several other algorithms. Althoug... View full abstract»

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  • Computing integral points in convex semi-algebraic sets

    Publication Year: 1997, Page(s):162 - 171
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (704 KB)

    Let Y be a convex set in Rk defined by polynomial inequalities and equations of degree at most d⩾2 with integer coefficients of binary length l. We show that if Y∩Zk≠θ, then Y contains an integral point of binary length ldO((k4)). For fixed k, our bound implies a polynomial-time algorithm for computing an integral point y∈Y. In part... View full abstract»

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  • Randomized and deterministic algorithms for the dimension of algebraic varieties

    Publication Year: 1997, Page(s):36 - 45
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (848 KB)

    We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NP-complete in the Blum-Shub-Smale model of computation over C, that it admits a sO(1)DO(n) deterministic algorithm, and that for systems with integer coefficients it is in the Arthur-Merlin class under the Generalized Riemann Hypothesi... View full abstract»

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  • Improved bounds on planar k-sets and k-levels

    Publication Year: 1997, Page(s):156 - 161
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (476 KB)

    We prove an O(nk1/3) upper bound for planar k-sets. This is the first considerable improvement on this bound after its early solutions approximately twenty seven years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k-levels in arrangements of line segments, k convex polygons in the union of n lines, parametric minimum spanning tr... View full abstract»

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  • Hamiltonian cycles in solid grid graphs

    Publication Year: 1997, Page(s):496 - 505
    Cited by:  Papers (7)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 KB)

    A grid graph is a finite node induced subgraph of the infinite two dimensional integer grid. A solid grid graph is a grid graph without holes. For general grid graphs, the Hamiltonian cycle problem is known to be NP complete. We give a polynomial time algorithm for the Hamiltonian cycle problem in solid grid graphs, resolving a longstanding open question posed by A. Itai et al. (1982). In fact, ou... View full abstract»

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  • Flows in undirected unit capacity networks

    Publication Year: 1997, Page(s):32 - 34
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (252 KB)

    We describe an O(min(m, n3/2)m1/2)-time algorithm for finding maximum flows in undirected networks with unit capacities and no parallel edges. This improves upon the previous bound of Karzanov and Even and Tarjan when m=ω(n3/2), and upon a randomized bound of Karger when υ=Ω(n7/4/m 1/2) View full abstract»

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  • Exploiting locality for data management in systems of limited bandwidth

    Publication Year: 1997, Page(s):284 - 293
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1120 KB)

    This paper deals with data management in computer systems in which the computing nodes are connected by a relatively sparse network. We consider the problem of placing and accessing a set of shared objects that are read and written from the nodes in the network. These objects are, e.g., global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in ... View full abstract»

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  • A 2-approximation algorithm for the directed multiway cut problem

    Publication Year: 1997, Page(s):548 - 553
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (428 KB)

    A directed multiway cut separates a set of terminals s1,...,sκ in a directed capacitated graph G=(V, E). Finding a minimum capacity directed multiway cut is an NP-complete problem. We give a polynomial-time algorithm that achieves an approximation factor of 2 for this problem. This improves the result of Garg, Vazirani and Yannakakis (1994) who gave an algorithm that ac... View full abstract»

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  • Pattern matching with swaps

    Publication Year: 1997, Page(s):144 - 153
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (812 KB)

    Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T' of T is a length n string derived from T by a series of local swaps, (i.e. t' l←tl+1 and t'l+1←tl) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of fi... View full abstract»

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  • Edge-connectivity augmentation preserving simplicity

    Publication Year: 1997, Page(s):486 - 495
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB)

    Given a simple graph G=(V, E), the goal is to find a smallest set F of new edges such that G=(V, E∪F) is κ edge connected and simple. Very recently this problem was shown to be NP hard by T. Jordan (1997). We prove that if OPTPκ is high enough-depending on κ only-then OPTSκ=OPTPκ holds, where OPT View full abstract»

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  • A faster deterministic algorithm for minimum spanning trees

    Publication Year: 1997, Page(s):22 - 31
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (860 KB)

    A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented. Its running time is O(m α log α), where α=α(m,n) is a functional inverse of Ackermann's function and n (resp. m) is the number of vertices (resp. edges). This improves on the previous, ten-year old bound of (roughly) O(m log log* m) View full abstract»

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  • Parallelizing elimination orders with linear fill

    Publication Year: 1997, Page(s):274 - 283
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1080 KB)

    This paper presents an algorithm for finding parallel elimination orders for Gaussian elimination. Viewing a system of equations as a graph, the algorithm can be applied directly to interval graphs and chordal graphs. For general graphs, the algorithm can be used to parallelize the order produced by some other heuristic such as minimum degree. In this case, the algorithm is applied to the chordal ... View full abstract»

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  • Buy-at-bulk network design

    Publication Year: 1997, Page(s):542 - 547
    Cited by:  Papers (46)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (452 KB)

    The essence of the simplest buy-at-bulk network design problem is buying network capacity “wholesale” to guarantee connectivity from all network nodes to a certain central network switch. Capacity is sold with “volume discount”: the more capacity is bought, the cheaper is the price per unit of bandwidth. We provide O(log2n) randomized approximation algorithm for ... View full abstract»

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  • Number-theoretic constructions of efficient pseudo-random functions

    Publication Year: 1997, Page(s):458 - 467
    Cited by:  Papers (31)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (908 KB)

    We describe efficient constructions for various cryptographic primitives (both in private-key and in public-key cryptography). We show these constructions to be at least as secure as the decisional version of the Diffie-Hellman assumption or as the assumption that factoring is hard. Our major result is a new construction of pseudo-random functions such that computing their value at any given point... View full abstract»

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  • Optimal suffix tree construction with large alphabets

    Publication Year: 1997, Page(s):137 - 143
    Cited by:  Papers (54)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 KB)

    The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. Weiner (1973), who introduced the data structure, gave an O(n)-time algorithm for building the suffix tree of an n-character string drawn from a constant size alphabet. In the comparison model, there is a trivial Ω(n log n)-time lower bound based on sorting, and Weiner's algorithm matches this bo... View full abstract»

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  • A concrete security treatment of symmetric encryption

    Publication Year: 1997, Page(s):394 - 403
    Cited by:  Papers (118)  |  Patents (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (952 KB)

    We study notions and schemes for symmetric (ie. private key) encryption in a concrete security framework. We give four different notions of security against chosen plaintext attack and analyze the concrete complexity of reductions among them, providing both upper and lower bounds, and obtaining tight relations. In this way we classify notions (even though polynomially reducible to each other) as s... View full abstract»

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  • Finding an even hole in a graph

    Publication Year: 1997, Page(s):480 - 485
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (492 KB)

    A hole in a graph is a chordless cycle of length greater than three. In this paper we present a decomposition theorem for graphs that contain no even hole. This theorem yields a polytime algorithm to recognize whether a graph contains an even hole View full abstract»

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  • Constant depth circuits and the Lutz hypothesis

    Publication Year: 1997, Page(s):595 - 604
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (976 KB)

    Resource-bounded measure theory is a study of complexity classes via an adaptation of the probabilistic method. The central hypothesis in this theory is the assertion that NP does not have measure zero in Exponential Time. This is a quantitative strengthening of NP≠P. We show that the analog in P of this hypothesis fails dramatically. In fact, we show that NTIME[n1/11] has measure ze... View full abstract»

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  • The analysis of a list-coloring algorithm on a random graph

    Publication Year: 1997, Page(s):204 - 212
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (692 KB)

    We introduce a natural k-coloring algorithm and analyze its performance on random graphs with constant expected degree c (Gn,p=cn/). For k=3 our results imply that almost all graphs with n vertices and 1.923 n edges are 3-colorable. This improves the lower bound on the threshold for random 3-colorability significantly and settles the last case of a long-standing open question of Bolloba... View full abstract»

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  • The minimization problem for Boolean formulas

    Publication Year: 1997, Page(s):575 - 584
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (680 KB)

    We investigate the computational complexity of the minimization problem for Boolean formulas. Depending on the definition, these problems are trivially in Σ2P or II2 P, and these are the best upper bounds known. The only previously known lower bounds are also trivial, and are coNP lower bounds at best, thus leaving quite a large gap between the upp... View full abstract»

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